1. Cell-cycle control Chapter 7 of Aguda & Friedman Amanda Galante Cancer Dynamics RIT September 25, 2009

2. Cell-cycle checkpoints Restriction point – Regulate initiation of DNA replication G2-M checkpoint – Checks DNA damage Spindle checkpoint – Checks chromosome alignment

3. Restriction Point ‘Commitment point’ for DNA replication R point – time after which cell will enter S phase, even in absence of growth factors Many cancers involve malfunctions of this checkpoint

4. G2 DNA Damage Checkpoint (G2DDC) Need to understand how coupled PD (phosphorylation- dephosphorylation) cycles work Need to establish bistability

5. PD cycle simple example

6. Transcritical Bifurcation Point

7. Two PD cycles Note that the eigenvalues of the Jacobian are both negative, implying a stable s.s. Could be unstable if That is, we need a destabilizing feedback loop.

8. Coupled PD cycles Transcritical bistability condition:

9. Applied to G2DDC

10. Results of G2DDC model Made up rate parameters (not experimentally available) Was able to show transcritical bistability as Note that MPF and Cdc25 become active at same time – ‘hallmark of transcritical bifurcation in positively coupled cyclic reactions’

11. PD cycle conclusions Established existence of transcritical bifurcation point for two coupled PD cycles – Allows system to ‘check whether all components are ready for the next cell cycle event’ MPF, Cdc25, Wee1 coupled PD cycles can be shown to generate bistability when including other reactions Also applicable to R point for cyclin E/CDK2 and Cdc25a

12. Mitotic spindle checkpoint Wikipedia - Kinetochore

13. Model Assumptions Final kinetochore attachment Cell-cycle progression triggered by a protein c * c diffuses throughout nucleus ρ = kinetochore radius (0.01 µm) R = nucleus radius (1 µm) D = diffusivity of c (1 µm 2 /s)

14. Model Objectives 1.After final kinetochore attachment, a protein c which was previously in an inhibited state c *, becomes sufficiently activated at time T b < 3 minutes 2.At steady state, c is predominantly in an inhibited state (want at least 90% inhibited, or A c <0.1). In this way, the system resets itself.

15. Model framework Doncic 2005

17. Summary: T b = 1.5 min – good! A = 0.4 (i.e. 40% of c molecules are inhibited) -- too high Direct Inhibition Model

18. Summary: T b = not happening… A < 0.1 “Self-Propagating Inhibition” Model

19. Summary: T b = 2.5 min A = 0.05 (i.e. the system resets itself) “Emitted Inhibition” Model

20. Varying parameters

21. Conclusions of Mitotic Spindle Checkpoint Model Single unattached kinetochore activating protein is a matter of speculation Illustrates the impact of temporal & spatial constraints Were able to develop a model which met the objectives – ‘Emitted Inhibition Model’

22. References Aguda, BD & A Friedman. Models of Cellular Regulation. Oxford University Press, 2008. Aguda, BD. (1999) ‘Instabilities in phosphorylation-dephosphorylation cascades and cell cycle checkpoints,’ Oncogene 18, 2846-2851. Aguda, BD. (1999) ‘A quantitative analysis of the kinetics of the G2 DNA damage checkpoint system,’ PNAS 96, 11352-11357. Doncic, A, Ben-Jacob, E and N Barkai. (2006) ‘Evaluating putative mechanisms of the mitotic spindle checkpoint,’ PNAS 102, 6332- 6337. Other picture references Wikipedia http://www.mun.ca/biology/desmid/brian/BIOL2060/BIOL2060- 19/CB19.html http://www.mun.ca/biology/desmid/brian/BIOL2060/BIOL2060- 19/CB19.html